In the present paper, natural convection heat transfer of CuO-water nanofluid subjected to a uniform magnetic field within an enclosed cavity considering of Brownian motion is studied by adopting the lattice Boltzmann Model. The left wavy wall is heated sinusoidal, while the right flat wall is maintained at the constant temperature of Tc. The top and the bottom horizontal walls are smooth and insulated against heat and mass. The variation of density is slight thus hydrodynamics and thermal fields equation are coupled using the Boussinesq approximation. The density and energy distribution are both solved by D2Q9 model. In this paper, the influence of pertinent parameters such as solid volume fraction of nanoparticles, Rayleigh number, Hartmann number and wavy-wall geometry parameters on flow and heat transfer fields are investigated. Results show that the heat transfer increases with the increment of Rayleigh number and nanoparticles volume fraction, but it decreases by the increment of the Hartmann number. The enhancement of magnetic field augments or plummets the effect produced by the presence of nanoparticles at different Rayleigh numbers. In addition, it is shown that for a fixed Rayleigh number and Hartmann number, the heat transfer performance depends on tuning the wavy-surface geometry parameters. The greatest effect of nanoparticles is observed by considering the role of Brownian motion. This study can, provide useful insight for enhancing the convection heat transfer performance within enclosed cavities with wavy-wall surfaces and sinusoidal temperature distribution under influence of magnetic field.